eBook - PDF

Geometry Of Mobius Transformations: Elliptic, Parabolic And Hyperbolic Actions Of Sl2(r) (With Dvd-rom)

Name: Geometry Of Mobius Transformations: Elliptic, Parabolic And Hyperbolic Actions Of Sl2(r) (With Dvd-rom)
ISBN: 9781848168596

Elliptic, Parabolic and Hyperbolic Actions of SL2(R)(With DVD-ROM)

Vladimir V Kisil,

208 pages
English
PDF
Available on iOS & Android

eBook - PDF

Geometry Of Mobius Transformations: Elliptic, Parabolic And Hyperbolic Actions Of Sl2(r) (With Dvd-rom)

Elliptic, Parabolic and Hyperbolic Actions of SL2(R)(With DVD-ROM)

Vladimir V Kisil,

About this book

This book is a unique exposition of rich and inspiring geometries associated with Möbius transformations of the hypercomplex plane. The presentation is self-contained and based on the structural properties of the group SL2(R). Starting from elementary facts in group theory, the author unveils surprising new results about the geometry of circles, parabolas and hyperbolas, using an approach based on the Erlangen programme of F Klein, who defined geometry as a study of invariants under a transitive group action.The treatment of elliptic, parabolic and hyperbolic Möbius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers which represent all non-isomorphic commutative associative two-dimensional algebras with unit. The hypercomplex numbers are in perfect correspondence with the three types of geometries concerned. Furthermore, connections with the physics of Minkowski and Galilean space-time are considered.

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Yes, you can access Geometry Of Mobius Transformations: Elliptic, Parabolic And Hyperbolic Actions Of Sl2(r) (With Dvd-rom) by Vladimir V Kisil in PDF and/or ePUB format, as well as other popular books in Biological Sciences & Science General. We have over one million books available in our catalogue for you to explore.